1. Field of the Invention
The present invention relates to an optical branching filter for causing light of desired wavelengths to branch off, which is suitable for a wavelength-division multiplexing optical communication, for example, and particularly to an optical multilayered-film filter wherein dielectric thin films different in refractive index from one another are stacked on one another in a multilayer form.
2. Description of the Related Art
The development of wavelength division multiplexing (WDX) has recently been pursued as a new technique corresponding to a leap increase in the capacity of an optical communication. However, there has been a demand for a further increase in the number of wavelength multiplex or multiples. Since light of desired wavelengths are selectively used in such an optical communication, an optical branching filter formed of a dielectric multilayered film in which two to three types of different dielectric thin films are alternately laminated on each other, is utilized.
Such an optical multilayered-film filter will be described below.
FIG. 6 is an explanatory view showing a structure of a conventional optical multilayered film.
When no absorption occurs in the film, a reflection power or reflectivity (R) and an amplitude reflection power rp+1,0 of light incident from a multilayered film corresponding to a p+1 layer on a substrate having a refractive index (n0) have the following relation. EQU R.sub.p+1,0 =.vertline.r.sub.p+1,0 .vertline..sup.2 (1)
With the amplitude reflection power of rp+1,0, the following equation is satisfied. ##EQU1## In the equation, dp and rp+1, p respectively indicate a phase and an amplitude reflection power between the p+1 layer and p layer. The following relation is given: ##EQU2## l indicates the wavelength of incident light, and np and dp indicate a refractive index of a p layer thin film and the optical thickness thereof respectively. fp indicates a refractive angle of light in the p layer. According to the Fresnel law, the following is given: ##EQU3## where the following equations are established upon s polarization and p polarization: EQU u.sub.i =n.sub.i cos .phi..sub.i (i=0,1,2 . . . ) (5) EQU u.sub.i =n.sub.i /cos .phi..sub.i (i=0,1,2 . . . ) (5)
A graphical method and an analytical synthetic method have heretofore been used to optimize a laminated structure of the optical multilayered film with respect to an arbitrary optical characteristic. It has been recently common practice to perform automatic calculations using a personal computer.
A further description will next be made of such a conventional optical multilayered-film filter with reference to FIGS. 7A, 7B and FIG. 3. FIG. 7A is a diagram showing the relationship between the number of layers and a refractive index for an optical multilayered-film filter in which dielectric thin films having high and low refractive indices are alternately stacked on each other. FIG. 7B is a diagram showing the result of calculation of a transmission characteristic for the optical multilayered film filter shown in FIG. 7A. FIG. 3 is a diagram illustrating a material of a film and an index of refraction thereof.
Such a conventional optical multilayered-film filter shown in FIG. 7A is formed by alternately laminating a high-refractive index dielectric thin film H and a low-refractive index dielectric thin film L on one another. Here, H and L denote TiO.sub.2 and SiO.sub.2 films having optical characteristics shown in FIG. 3, respectively. Upon calculation of a transmission spectrum, an incident angle of light was defined as 0 (vertical incidence) and a center wavelength thereof was defined as 730 nm. While the conventional optical multilayered-film filter has a reflection power of approximately 100% in a reflection band having the center wavelength (730 nm), it has a problem in that many interference peaks exist in a transmission band. It was therefore difficult to obtain a high-accuracy optical filter.
On the other hand, a rugate filter having a structure in which a refractive index relative to the direction of the thickness of each dielectric thin film is continuously and periodically varied according to a since function or the like, has been known as one for improving the optical characteristic of the aforementioned conventional optical multilayered-film filter.
The rugate filter illustrated as the second conventional example will be explained with reference to FIGS. 8A and 8B. FIG. 8A is a diagram showing the number of layers and a refractive index for the rugate filter, and FIG. 8B is a diagram showing the result of calculation of a transmission spectrum of the rugate filter shown in FIG. 8A, respectively. In order to make a comparison with the configuration of the optical multilayered-film filter in which the aforementioned high and low refractive-index thin films are alternately stacked on each other, the relationship between the refractive index and the number of films laminated was illustrated in FIG. 8A with the thickness corresponding to one cycle of the sine wave being regarded as two layers of alternate multilayered films. The dependency of the refractive index (n) of the rugate filter on the optical thickness (x) thereof can be given by the following equation: EQU n(X) =n.sub.o +n.sub.1 sin(2.pi.X/P) (7)
where n0 and n1 indicate an average refractive index and the amplitude of a change in refractive index respectively, and P indicates the thickness in one sine cycle. As shown in FIG. 8A, the rugate filter has a structure in which the refractive index continuously and periodically varies in its thickness direction according to the since function.
As is apparent from FIG. 8B, the rugate filter restrains the interference in a transmission region and decreases even a harmonic reflection peak of a low wavelength range as compared with the optical multilayered-film filter in which the high-refractive index layers are alternately stacked on each other, but cannot eliminate a reflection peak lying in the vicinity of a reflection band.
Therefore, the rugate filter needs other functions for adjusting or controlling its optical characteristic upon filter design to solve the interference peak in the vicinity of the reflection band. For instance, the quintic function and the Fourier function or the like are added to the structure of the rugate filter to thereby allow an improvement in the optical characteristic of a broadband reflection filter. Since, however, the configuration of the filter becomes extremely complex, the fabrication thereof is made more difficult.
As described above, the conventional optical multilayered-film filter in which the high-refractive index film and the low-refractive index film are alternately laminated on each other, has a problem in that it is difficult to satisfy required performance such as a narrow band width, stability with respect to a change in temperature, etc.
Further, the rugate filter has a problem in that the configuration thereof is complex, the control for continuously varying the refractive index in accordance with the designed values and forming the film with high accuracy is difficult, its productivity is low, and it is difficult to provide the rugate filter with stable quality and at low cost.